IBCCES is really just approving that one submitted documentation, not so much reviewing the contents of that documentation for merit. It doesn't take a medical degree to determine:
1. documentation is from an acceptable source (medical provider, government entity or school IEP or 504)
2. documentation includes:
a. medical diagnosis and/or
b. explanation of the needs and accommodations
It really sounds like #2 is fairly loosely determined; I think they are primarily approving #1.
The theme park employees are still the ones who will approve/deny accommodations, and they do so without access to anything you submitted.
I'm not defending or recommending the business. But it is a legitimate company that has been doing this for several years for many theme parks. Anyone who thinks a doctor should be reviewing your info isn't going to find that anywhere at any business -- I don't believe the DMV contracts physicians to review HA tag applications, either.
Everyone is free to make their own decision as to whether they are comfortable enough to go through this process.